PHOENIX (AP) -- Democrat Ron Barber has won a full term representing Arizona's 2nd Congressional District, squeaking out a win over Republican Martha McSally and giving Democrats a sweep of the state's three competitive races for U.S. House seats.

Voters decisively picked Barber to fill out the remainder of former Rep. Gabrielle Giffords term in a special election in June, but last week's election was for a full term and was so tight it took until Saturday before a winner was clear. Barber and McSally each held leads since election night, with a difference of only a few dozen votes at times, before Barber steadily began pulling ahead.

By late Friday, Barber had a 1,402-vote margin with more than 285,000 votes cast in the race. Only about 15,000 provisional ballots remain to be counted in Pima County, although not all are in the 2nd District. An Associated Press analysis determined Barber's lead could not be overcome.

"I'm really proud and honored that I've been given another opportunity to serve," Barber told the AP on Saturday. "I never expected to be in Congress. When I won the special election I was thrilled about that and now I have two years to get some work done, and I really understand what the issues are nationally and locally and I'm going to be working hard on those."

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Barber said McSally called and congratulated him at midmorning, and conceded the race.

McSally planned a 2 p.m. Saturday press conference in Tucson. Her campaign manager could not be immediately reached Saturday morning.

Barber is Giffords' former district director and she endorsed his candidacy. He touted his lengthy history in the district, his moderate views and his strong backing for veterans and border security.

He was with Giffords at a constituent meet-and-greet in Tucson in January 2011 when a mentally ill man, Jared Lee Loughner, opened fire, killing six and wounding 13 others. Giffords was hit in the head and ultimately had to step down from her seat, while Barber was hit in the thigh and cheek.

McSally is a former Air Force pilot who was making her first run for political office. Her surprisingly close finish showed that the 2nd District remains a true swing district that either party can win with the right candidate.

The district, which resembles Arizona's old 8th Congressional District before redistricting, covers parts of Tucson and Pima County and all of Cochise County.

Barber's victory means Democrats have the majority of the state's congressional delegation, holding five of the state's nine U.S. House seats, while Republicans' only congressional victories in Arizona were in districts safe for GOP candidates.

The Republicans had a 5-3 advantage in the state's U.S. House delegation going into the Nov. 6 election, which filled a new ninth seat.

Democrat Krysten Sinema won the new Phoenix-area 9th District over former Paradise Valley mayor Vernon Parker, while Democrat Ann Kirkpatrick regained her old congressional seat by beating Republican Jonathan Paton in the 1st District.

With Rep. Jeff Flake's victory over Democrat Richard Carmona, Republicans will continue to hold both of the state's U.S. House seats.

Barber said he was not surprised that the race was so tight, considering the state redistricting commission intentionally designed it and two others -- the ones won by Sinema and Kirkpatrick -- to be winnable by either party. The other five Arizona congressional seats are basically winnable by only one party, four Republican seats and two Democratic.

"We just worked really hard to get our message out, and to make sure that we could say who we are and what I'm about to voters," he said.